Simplify to lowest terms. $\dfrac{27}{90}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 27 and 90? $27 = 3\cdot3\cdot3$ $90 = 2\cdot3\cdot3\cdot5$ $\mbox{GCD}(27, 90) = 3\cdot3 = 9$ $\dfrac{27}{90} = \dfrac{3 \cdot 9}{ 10\cdot 9}$ $\hphantom{\dfrac{27}{90}} = \dfrac{3}{10} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{27}{90}} = \dfrac{3}{10} \cdot 1$ $\hphantom{\dfrac{27}{90}} = \dfrac{3}{10}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{27}{90}= \dfrac{3\cdot9}{3\cdot30}= \dfrac{3\cdot 3\cdot3}{3\cdot 3\cdot10}= \dfrac{3}{10}$